Kentucky Gov. Steve Beshear says he supports the expansion of Medicaid in his state under President Obama’s health care law, a decision that would extend coverage to 308,000 residents.

Mr. Beshear, who until Thursday was the last Democratic governor to make a decision on the expansion, deemed it “the single-most important decision in our lifetime for improving the health of Kentuckians.”

Kentucky had been among the final holdouts in deciding whether or not to extend the benefits to those earning up to 138 percent of the federal poverty level.

Twenty-eight states and the District of Columbia support the expansion, 20 oppose it and Kansas and South Dakota are still weighing their options, according to the nonpartisan Kaiser Family Foundation.

The state legislature still could block Kentucky’s expansion, a possibility that has become a reality for other governors who tried to pitch the measure to right-leaning lawmakers.

Florida Gov. Rick Scott is considering whether or not to call a special session in Tallahassee, after legislators left town without agreeing to the expansion.

Last June, the Supreme Court said states could expand the program under the Affordable Care Act without forfeiting their existing federal funding for the program.

The federal government has promised to pay for 100 percent of the expansion population in 2014-2016, before gradually scaling back its contribution to 90 percent in 2020 and thereafter.

Governors who declined the Medicaid dollars say the federal-state entitlement will eventually eat up their budgets, and Washington cannot be trust to live up to its end of the bargain.

According to Mr. Beshear’s estimates, the expansion will create 17,000 jobs and inject $15.6 billion into his state’s economic between fiscal years 2014 and 2021.

“My only concern was the cost,” Mr. Beshear said. “We have now done the exhaustive research — and our conclusion matched what most other states have found: by expanding Medicaid, Kentucky will come out ahead in terms of both health outcomes and finances. In fact, if we don’t expand Medicaid, we will lose money.”